Problem: A circle has a circumference of $12\pi$. It has an arc of length $11\pi$. What is the central angle of the arc, in radians? ${12\pi}$ ${\dfrac{11}{6}\pi}$ $\color{#DF0030}{11\pi}$
Solution: The ratio between the arc's central angle $\theta$ and $2 \pi$ radians is equal to the the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{2 \pi} = \dfrac{s}{c}$ $\dfrac{\theta}{2 \pi} = 11\pi \div 12\pi$ $\dfrac{\theta}{2 \pi} = \dfrac{11}{12}$ $\theta = \dfrac{11}{12} \times 2 \pi$ $\theta = \dfrac{11}{6}\pi$ radians